A MIMO (Multiple Input Multiple Output) technique that spatially multiplexes and transmits a plurality of streams using a plurality of transmitting/receiving antennas has been put to practical use. Transmission capacity can be increased by this MIMO transmission. As one of MIMO transmission schemes, there is available an eigenmode MIMO transmission scheme that can use, to the utmost, the potential transmission capacity of a transmission path when the state of a transmission path can be grasped on the transmission side.
In the eigenmode MIMO transmission scheme, assuming the transmission path characteristic as H as shown in Expression 1, the transmission path characteristic is singular-value-decomposed as preprocessing of eigenmode transmission.H=UΣVH  (Expression 1)(H on the upper right side of V indicates complex conjugate transpose)
In Expression 1, U denotes a left singular value matrix, V denotes a right singular value matrix, and Σ is a matrix indicating an eigenvalue (√λk) whose diagonal component is H as shown in Expression 2. In addition, the elements of each matrix are complex numbers. In the following description, the elements of a matrix and a vector are assumed to be complex numbers unless otherwise stated.Σ=diag{√{square root over (λ1)}√{square root over (λ2)} . . . √{square root over (λL)}}  (Expression 2)where λ1>λ2> . . . >λL.
In eigenmode MIMO transmission, L stream vectors S=[S1 S2 . . . SL]T are used as streams for performing information transmission. Information is transmitted by placing the information on the amplitude and phase of the stream vectors S. After multiplying the stream vectors S by the right singular value matrix V, a transmission signal vector X is generated. Furthermore, the transmission power of each stream is appropriately distributed by using the principle called a water injection theorem, where by the increase in the transmission capacity can be expected.
Assuming that the power distribution matrix is P=diag{√{square root over (p1)} √{square root over (p2)} . . . √{square root over (pn-1)}}, the transmission signal vector X is represented by Expression 3.X=VPS  (Expression 3)
The processing shown in Expression 3 is referred to as precoding processing on the stream vectors S. The transmission signal vector X after precoding is transmitted from each transmission antenna.
The reception signal vector Y is a signal obtained by adding a thermal noise vector N (where a variance is σ2) after the transmission signal vector X passes through the transmission path matrix H.Y=HX+N  (Expression 4)
Expression 1 and Expression 3 are substituted into Expression 4 to obtain Expression 5.Y=(UΣVH)(VPS)+N Y=UΣPS+N  (Expression 5)
The transmission stream vector S indicated in Expression 6 is estimated by subjecting the reception signal vector Y represented by Expression 5 to spatial filter processing for decomposing the reception signal vector Y for each stream. The spatial filter processing can be realized by multiplying the reception signal vector Y by a complex conjugate transpose matrix UH of the left singular value matrix.Ŝ=UHY Ŝ=UH(UΣPS+N)Ŝ=ΣPS+UHN  (Expression 6)
In Expression 6, the first term ΣPS on the right side denotes a signal component, and the second term UHN denotes a noise component. The details of the signal component of the first term are shown in Expression 7.
                              Σ          ⁢                                          ⁢          PS                =                              [                                                                                                      λ                      1                                                                                        0                                                  0                                                  0                                                                              0                                                                                            λ                      2                                                                                        0                                                  0                                                                              ⋮                                                  ⋮                                                  ⋮                                                  ⋮                                                                              ⋮                                                  ⋮                                                  ⋮                                                  ⋮                                                                              0                                                  0                                                  0                                                                                            λ                      L                                                                                            ]                    ⁢                                                                 [                                                                  ⁢                                                                                                                              P                          1                                                                                                            0                                                              0                                                              0                                                                                                  0                                                                                                                P                          2                                                                                                            0                                                              0                                                                                                  ⋮                                                              ⋮                                                              ⋮                                                              ⋮                                                                                                  ⋮                                                              ⋮                                                              ⋮                                                              ⋮                                                                                                  0                                                              0                                                              0                                                                                                                P                          L                                                                                                                    ]                            ⁢                                                                                                           [                                                                                                                                  s                              1                                                                                                                                                                                          s                              2                                                                                                                                                            ⋮                                                                                                                                                              s                              L                                                                                                                          ]                                        ⁢                                                                                  ⁢                                                                                  ⁢                    Σ                    ⁢                                                                                  ⁢                    PS                                    =                                      [                                                                                                                                                                                                                        λ                                  1                                                                ⁢                                                                  P                                  1                                                                                                                      ⁢                                                          s                              1                                                                                                                                                                                                                                                                                                        λ                                  2                                                                ⁢                                                                  P                                  2                                                                                                                      ⁢                                                          s                              2                                                                                                                                                                            ⋮                                                                                                                                                                                                                                                  λ                                                                      n                                    -                                    1                                                                                                  ⁢                                                                  P                                                                      n                                    -                                    1                                                                                                                                                        ⁢                                                          s                                                              n                                -                                1                                                                                                                                                                          ]                                                                                                          (                  Expression          ⁢                                          ⁢          7                )            
Similarly, the details of the noise component of the second term are shown in Expression 8.
                                          U            H                    ⁢          N                =                              U            H                    ⁡                      [                                                                                n                    1                                                                                                                    n                    2                                                                                                ⋮                                                                                                  n                                          n                      -                      1                                                                                            ]                                              (                  Expression          ⁢                                          ⁢          8                )            
In Expression 8, [n1 n2 . . . nn−]T is a thermal noise exhibiting a Gaussian distribution, the average value of each element is 0, and the variance is σ2. Since UH is a unitary matrix, there is no such thing as emphasizing this noise level.
The SN ratio of each stream is calculated using Expression 7 and Expression 8. Assuming that the SN ratio of the kth stream is SNRk, Expression 9 is obtained.
                                          SNR            k                    =                                                    λ                k                            ⁢                              P                k                            ⁢                              E                ⁡                                  [                                                                                                          s                        k                                                                                    2                                    ]                                                                    σ              2                                      ⁢                                  ⁢                              SNR            k                    =                                    λ              k                        ⁢                          P              k                        ⁢                                          P                s                                            σ                2                                                    ⁢                                  ⁢                              where            ⁢                                                  ⁢                          P              s                                =                                    E              ⁡                              [                                                                                                s                      k                                                                            2                                ]                                      .                                              (                  Expression          ⁢                                          ⁢          9                )            
As shown in Expression 9, if appropriate precoding processing is performed, the SN ratio of each stream becomes a value corresponding to the eigenvalue of the transmission path and the power distribution matrix. Although not described in detail, according to the theory of the water injection theorem of the eigenmode MIMO transmission scheme, it is possible to transmit a large amount of information by performing large power distribution √Pk for a stream having a large eigenvalue √λk.
Therefore, by allocating a modulation scheme with a large multi-value number (for example, 256 QAM (Quadrature Amplitude Modulation), etc.), it is possible to make maximum use of the potential transmission capacity of the transmission path. Conversely, since it is impossible to transmit a lot of information with a stream having a small eigenvalue, a modulation scheme with a small multi-value number (for example, QPSK (Quadrature Phase Shift Keying), etc.) is allocated.
By the eigenmode transmission MIMO scheme described above, it is possible to perform transmission with the maximum transmission capacity for the transmission path.
In addition, when the eigenmode MIMO transmission is applied to a wide frequency bandwidth, the characteristics of the transmission path often become different for each frequency ω due to the influence of multipath or the like. Therefore, the transmission path characteristic matrix H(ω) is represented by a function of the frequency ω. In an environment having such frequency characteristics, it is possible to optimize the transmission capacity by appropriately performing the above-described stream distribution for each frequency (ω). In order to perform optimization on a frequency-by-frequency basis, an OFDM (Orthogonal Frequency Division Multiplexing) modulation scheme that performs transmission while making narrowband multiple subcarriers orthogonal to each other is used, whereby stream distribution suitable for the transmission path H (ω can be performed for each subcarrier (or on a unit of a plurality of subcarriers).
By the way, in the OFDM scheme, when the phases of a plurality of subcarriers coincide with each other, there is a tendency that a large amplitude peak (instantaneous peak) appears.
On the other hand, in the case of a general power amplifier, when a signal with a large amplitude is inputted and output power comes closes to a saturated state, nonlinear distortion occurs. This also applies to a power amplifier used for amplifying a carrier on the transmission side of a transmission system. As in the case of the above-described OFDM scheme, if a large amplitude peak is included in the time waveform of an input signal, nonlinear distortion of a power amplifier occurs. Due to this distortion, the EVM (Error Vector Magnitude: modulation accuracy) of all streams is deteriorated, and the bit error rate is increased. Furthermore, due to this nonlinear distortion, there is also posed a problem that power leakage out of a band occurs.
Although the problem attributable to the nonlinear distortion can be solved by increasing the back-off of the power amplifier, there is a tradeoff relationship that the efficiency of the power amplifier decreases. Thus, as a technique for reducing the instantaneous peak, a technique has been proposed in which filtering is performed on a peak exceeding a predetermined level of threshold value, thereby reducing the peak while suppressing out-of-band leakage (see, e.g., Patent Document 1, etc.).